1. Field of the Invention
The present invention relates to a charged particle beam drawing apparatus and proximity effect correction method thereof, wherein patterns corresponding to figures included in a drawing data are drawn in a drawing area of a workpiece by applying a charged particle beam to the workpiece, wherein a resist is applied to an upper surface of the workpiece.
2. Description of Related Art
As is known in the prior art, in a charged particle beam drawing apparatus, patterns corresponding to figures included in a drawing data (EB data) are drawn in a drawing area of a workpiece, such as a mask substrate (reticle) and a wafer, by applying a charged particle beam to the workpiece, wherein a resist is applied to an upper surface of the workpiece. For example, the charged particle beam drawing apparatus in the prior art is described in Japanese Unexamined Patent Publication No. 2003-318077. In the charged particle beam drawing apparatus described in Japanese Unexamined Patent Publication No. 2003-318077, a proximity effect correcting map having meshes is formed, the size of each mesh being 2 μm×2 μm, so that figures included in the drawing data (EB data) are placed in the proximity effect correcting map (see FIGS. 10(a) and 10(c), and paragraph 0095 of Japanese Unexamined Patent Publication No. 2003-318077). Then, in the charged particle beam drawing apparatus described in Japanese Unexamined Patent Publication No. 2003-318077, representative figures are formed, wherein area of a representative figure is equal to gross area of figures placed in a mesh (see FIG. 10(c) and paragraph 0096 of Japanese Unexamined Patent Publication No. 2003-318077). Then, in the charged particle beam drawing apparatus described in Japanese Unexamined Patent Publication No. 2003-318077, a proximity effect correction dose (optimum dose D(x)) of the charged particle beam in each mesh is calculated by solving proximity effect correction equations (see paragraph 0030 of Japanese Unexamined Patent Publication No. 2003-318077), wherein the size of each mesh is 2 μm×2 μm (see FIG. 10(d) and paragraphs 0041, 0044, 0072, and 0109 of Japanese Unexamined Patent Publication No. 2003-318077).
In detail, in the charged particle beam drawing apparatus described in Japanese Unexamined Patent Publication No. 2003-318077, when the proximity effect correction dose (optimum dose D(x)) of the charged particle beam in each mesh is calculated, the size of each mesh being 2 μm×2 μm, area of representative figure in each mesh is considered. Concretely, if area of representative figure in a mesh is large, namely, if area density of figures in the mesh is large, dose of the charged particle beam for drawing patterns corresponding to figures in the mesh is large, consequently, influence of backscattering on figures in surrounding meshes is large. If area of representative figure in a mesh is small, namely, if area density of figures in the mesh is small, dose of the charged particle beam for drawing patterns corresponding to figures in the mesh is small, consequently, influence of backscattering on figures in surrounding meshes is small.
A following equation (1) shows a relation among the accumulation energy of the charged particle beam accumulated in the resist by forward-scattering of the charged particle beam (which corresponds to the left portion of the left side of the equation (1)), the accumulation energy of the charged particle beam accumulated in the resist by backscattering of the charged particle beam (which corresponds to the right portion of the left side of the equation (1)), and sum of the accumulation energy of the charged particle beam accumulated in the resist (which corresponds to the right side of the equation (1)), in the typical charged particle beam drawing apparatus in the prior art, such as the charged particle beam drawing apparatus described in Japanese Unexamined Patent Publication No. 2003-318077.
                                                        D              ⁡                              (                x                )                                      2                    +                      η            ⁢                          ∫                                                ∫                  pattern                                ⁢                                                      D                    ⁡                                          (                                              x                        ′                                            )                                                        ⁢                                      g                    ⁡                                          (                                              x                        -                                                  x                          ′                                                                    )                                                        ⁢                                      ⅆ                                          x                      ′                                                                                                          =                              E            0                    ⁢                                                    ↙                                                                                                                                                    ⁢                                                                      constant                  ⁢                                                                          ⁢                  in                  ⁢                                                                          ⁢                  unit                                                                                                                          drawing                    ⁢                                                                                  ⁢                    area                                    ,                                                                                                      such                  ⁢                                                                          ⁢                  as                  ⁢                                                                          ⁢                  a                  ⁢                                                                          ⁢                  chip                                                                                        (        1        )            
In the equation (1), E0 (right side of the equation (1)) shows the accumulation energy of the charged particle beam accumulated in a position x in the resist. In detail, x shows a location vector. In the equation (1), D(x) shows the proximity effect correction dose of the charged particle beam applied from an optical column to the position x in the resist. The left portion (D(x)/2) of the left side of the equation (1) shows the accumulation energy of the charged particle beam accumulated in the position x in the resist, after the charged particle beam is applied from the optical column to the position x in the resist. Namely, the equation (1) means that a half (D(x)/2) of the dose D(x) of the charged particle beam applied from the optical column to the position x in the resist is accumulated in the position x in the resist. The right portion of the left side of the equation (1) shows the accumulation dose of the charged particle beam accumulated in the position x in the resist by proximity effect (backscattering), after the charged particle beam is applied from the optical column to positions x′ in a whole drawing area in the resist. In detail, in the equation (1), η shows a proximity effect correction coefficient, and g shows a proximity effect influence distribution. In the typical charged particle beam drawing apparatus in the prior art, Gaussian distribution (normal distribution) is used as the proximity effect influence distribution g. Following equations (2) to (8) show proximity effect correction equations used in the typical charged particle beam drawing apparatus in the prior art, such as the charged particle beam drawing apparatus described in Japanese Unexamined Patent Publication No. 2003-318077.
                              g          ⁡                      (                          x              -                              x                ′                                      )                          =                              1                          π              ⁢                                                          ⁢                              σ                2                                              ⁢                      exp            [                          -                                                                    (                                          x                      -                                              x                        ′                                                              )                                    2                                                  σ                  2                                                      ]                                              (        2        )                                          D          ⁡                      (            x            )                          =                              ∑                          n              =              0                        ∞                    ⁢                                          ⁢                                    d              n                        ⁡                          (              x              )                                                          (        3        )                                                      d            0                    ⁡                      (            x            )                          =                              E            0                                              1              /              2                        +                          η              ⁢                                                          ⁢                              U                ⁡                                  (                  x                  )                                                                                        (        4        )                                          E          0                =                              (                                          1                /                2                            +              η                        )                    ⁢                      D            base                                              (        5        )                                                      d            n                    ⁡                      (            x            )                          =                                                            η                ⁢                                                                  ⁢                                                      d                    0                                    ⁡                                      (                    x                    )                                                                              E                0                                      ⁡                          [                                                                                          d                                              n                        -                        1                                                              ⁡                                          (                      x                      )                                                        ⁢                                      U                    ⁡                                          (                      x                      )                                                                      -                                                      V                    n                                    ⁡                                      (                    x                    )                                                              ]                                ⁢                                          ⁢                      (                          n              ≥              1                        )                                              (        6        )                                          U          ⁡                      (            x            )                          =                              ∫            pattern                                                          ⁢                                    g              ⁡                              (                                  x                  -                                      x                    ′                                                  )                                      ⁢                                                  ⁢                          ⅆ              x                                                          (        7        )                                                      V            n                    ⁡                      (            x            )                          =                              ∫            pattern                                                          ⁢                                          ⁢                                                    ⅆ                                  n                  -                  1                                            ⁢                              (                                  x                  ′                                )                                      ⁢                          g              ⁡                              (                                  x                  -                                      x                    ′                                                  )                                      ⁢                          ⅆ                              x                ′                                                                        (        8        )            
An equation (3) corresponds to the equation 1 in paragraph 0030 of Japanese Unexamined Patent Publication No. 2003-318077. An equation (4) corresponds to the equation 2 in paragraph 0030 of Japanese Unexamined Patent Publication No. 2003-318077. An equation (6) corresponds to the equation 3 in paragraph 0030 of Japanese Unexamined Patent Publication No. 2003-318077. An equation (7) corresponds to the equation 4 in paragraph 0030 of Japanese Unexamined Patent Publication No. 2003-318077. An equation (8) corresponds to the equation 5 in paragraph 0030 of Japanese Unexamined Patent Publication No. 2003-318077. In the equation (2), a shows a standard deviation of the proximity effect influence distribution g. In the equation (5), Dbase shows a base dose of the charged particle beam. Namely, in the typical charged particle beam drawing apparatus in the prior art, such as the charged particle beam drawing apparatus described in Japanese Unexamined Patent Publication No. 2003-318077, the proximity effect correction dose D(x) of the charged particle beam in each mesh is calculated by solving the proximity effect correction equations (equations (2) to (8)) under the condition that the sum (the right side of the equation (1)) of the accumulation energy of the charged particle beam accumulated by forward-scattering (the left portion of the left side of the equation (1)) and the accumulation energy of the charged particle beam accumulated by backscattering (the right portion of the left side of the equation (1)) is constant in a unit drawing area, such as a chip, the unit drawing area being a part of the whole drawing area of the workpiece.
When patterns are drawn on the workpiece, a correction error can appear to the patterns. In detail, in one case, a correction error can appear to the patterns throughout the unit drawing area, such as a chip. In another case, a correction error can appear to the patterns locally in the unit drawing area, such as a chip. If a correction error, in which the actual width of linear patterns are smaller than the target width of the patterns, appears to the patterns throughout the unit drawing area, such as a chip, the correction error can be solved by increasing the proximity effect correction dose D(x) of the charged particle beam in each mesh, under the condition that the sum (the right side of the equation (1)) of the accumulation energy of the charged particle beam accumulated by forward-scattering (the left portion of the left side of the equation (1)) and the accumulation energy of the charged particle beam accumulated by backscattering (the right portion of the left side of the equation (1)) is constant in a whole unit drawing area, such as a chip, in the typical charged particle beam drawing apparatus in the prior art, such as the charged particle beam drawing apparatus described in Japanese Unexamined Patent Publication No. 2003-318077. If a correction error, in which the actual width of linear patterns are larger than the target width of the patterns, appears to the patterns throughout the unit drawing area, such as a chip, the correction error can be solved by decreasing the proximity effect correction dose D(x) of the charged particle beam in each mesh, under the condition that the sum (the right side of the equation (1)) of the accumulation energy of the charged particle beam accumulated by forward-scattering (the left portion of the left side of the equation (1)) and the accumulation energy of the charged particle beam accumulated by backscattering (the right portion of the left side of the equation (1)) is constant in a whole unit drawing area, such as a chip, in the typical charged particle beam drawing apparatus in the prior art, such as the charged particle beam drawing apparatus described in Japanese Unexamined Patent Publication No. 2003-318077.
However, when a correction error appears to the patterns locally in the unit drawing area, such as a chip, if the proximity effect correction dose D(x) of the charged particle beam in some meshes in the unit drawing area is changed, and if the proximity effect correction dose D(x) of the charged particle beam in another meshes in the unit drawing area is not changed in order to solve the correction error, the condition that the sum (the right side of the equation (1)) is constant in the whole unit drawing area, such as a chip, is not fulfilled. Accordingly, in the charged particle beam drawing apparatus in the prior art, such as the charged particle beam drawing apparatus described in Japanese Unexamined Patent Publication No. 2003-318077, the proximity effect correction dose D(x) of the charged particle beam in only some meshes in the unit drawing area cannot be changed, therefore, the correction error which appears to the patterns locally in the unit drawing area, such as a chip, cannot be solved. Consequently, in the prior art, when it is necessary to solve the correction error which appears to the patterns locally in the unit drawing area, such as a chip, a conventional lithography technology or computer lithography technology is used.
In the conventional lithography technology, if it is supposed that the correction error which appears to the patterns locally in the unit drawing area, such as a chip, is caused by resist process, such as resist application process, pre-bake process, development process, post-bake process, a simulation, in which the shape of patterns are gradually changed, is performed, so that the shape of patterns which are drawn, are made to correspond to the target shape of patterns. Accordingly, the correction error which appears to the patterns locally in the unit drawing area, such as a chip, is solved. However, in the conventional lithography technology, not only the dose of the charged particle beam is changed, but also a change of a whole mask process (resist process) is considered, in order to solve the correction error which appears to the patterns locally in the unit drawing area, such as a chip. Consequently, it is not easy to solve the correction error which appears to the patterns locally in the unit drawing area, such as a chip, in the conventional lithography technology.
In the computer lithography technology which is rapidly developing in recent years, the correction error which appears to the patterns locally in the unit drawing area, such as a chip, can be solved by selecting an optimum condition of mask pattern and optical system, and then, using a computer, and then, correcting mask process (resist process). However, in the computer lithography technology, it is necessary to consider a change of mask process model by considering a whole mask process (resist process), in order to solve the correction error which appears to the patterns locally in the unit drawing area, such as a chip. And large calculation cost is required because calculation time of the computer is enormous. Accordingly, it is not easy to solve the correction error which appears to the patterns locally in the unit drawing area, such as a chip, in the computer lithography technology.